There are several questions here on meta about "How to guide new users" and in particular "How to educate new users about accepting answers" (see 1, 2, 3, 4). A common approach seems to be to comment on the post, pointing to the FAQ or proposing a certain action.

1 Answer
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General

"How it works" section and "Tell me more" button is displayed on the first visit to any Stack Exchange site

Informed badge for reading the entire about page

Notifications about new privileges

Accepting Answers

Scholar badge for first accepted answer

+2 reputation for each accepted answers

"Don't forget you can mark this as the accepted answer by clicking its check mark" note when voting up an answer to your own question (screen shot)

"Have you considered accepting an answer or starting a bounty for this question?" note above questions without accepted answer on the questions page in your profile

Giving Feedback

Supporter badge for first up vote

Critic badge for first down vote

"Please consider adding a comment if you think this post can be improved" note when voting down without having commented first

Commentator badge when posting the 10th comment

Writing Good Posts

Editor formatting help is displayed by default

Improving Posts

Editor badge for first edit

"Are you sure you want to answer your question? Comment if you're trying to respond to an answer. Edit your question if you need to add more details." when trying to answer your own question (screen shot)

"Are you sure you want to add another answer? You could use the edit link to refine and improve your existing answer, instead." when trying to add an answer to a question you have already answered